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# Optimum System Design Using Rough Interval Multi-Objective De Novo Programming

## Authors

• Iftikhar Hussein Engineering Technical Collage, Middle Technical University, Baghdad, Iraq. https://orcid.org/0000-0003-3646-8054
• Hegazy Zaher Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt.
• Naglaa Ragaa Saeid Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt.
• Hebaa Sayed Roshdy Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt.

## Keywords:

De novo programming, Multi-objective linear programming, Optimum-path ratios, Optimal system design, Rough interval linear programming

## Abstract

The Multi-objective de novo programming method is an effective tool to deal with the optimal system design by determining the optimal level of resources allocation (RA) to improve the value of the objective functions according to the price of resources (the conditions are certainty). This paper suggested a new approach for solving uncertainty of De novo programming problems (DNP) using a combination model consisting of a rough interval multi-objective programming (RIMOP) and DNP, where coefficients of decision variables of objective functions and constraints are rough intervals (RIC). Three methods are used to find the optimal system design for the proposed model, the first method is the weighted sum method (WSM) which  is used before reformulating RIMOP (bi of constraints is known), WSM gives one ideal solution among the feasible solutions under each bound of sub-problem, the second method is Zeleny’s approach and the third method is the optimal path- ratios, methods (two and three) are used after formulating (RIMODNP) (bi of constraints is unknown), Zeleny’s approach gives one (alternative) optimal system design under each bound of sub-problem, while the optimal path- ratios method: after checking the bounds according to Shi’s theorem, determines whether the bounds of the proposed model are feasible or not, and then use the method, this method uses three types of ratios gives three (alternatives) under each bound of sub-problem. From the results, it is clear that the optimal path-ratios method is more efficient than others in solving the proposed model because it provides alternatives to the decision-maker (DM), it is noted that the proposed model is compatible with the conditions and theories of RIC. As a result, the proposed model is very suitable for conditions of uncertainty. Finally, applied example is also presented for the proposed model application.

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